To solve by the elimination method.
5x+7y=40,x=y+3
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To solve the given system of equations using the elimination method, follow these steps:
Step 1: Write down both equations of the system.
5x + 7y = 40 ... (Equation 1)
x = y + 3 ... (Equation 2)
Step 2: Choose one of the variables (x or y) to eliminate by manipulating the equations. In this case, let's eliminate the variable "x".
Step 3: Multiply Equation 2 by 5, so that the coefficients of "x" in both equations will be equal.
5(x) = 5(y + 3)
5x = 5y + 15 ... (Equation 3)
Step 4: Now, subtract Equation 3 from Equation 1.
(5x + 7y) - (5x) = (40) - (5y + 15)
7y - 5y = 40 - 5y - 15
2y = 25 - 5y ... (Equation 4)
Step 5: Rearrange Equation 4 to isolate "y".
2y + 5y = 25
7y = 25
y = 25/7
Step 6: Substitute the value of "y" (25/7) into either Equation 1 or Equation 2 to solve for "x". Let's use Equation 2.
x = (25/7) + 3
x = (25 + 21)/7
x = 46/7
So the solution to the system of equations is x = 46/7 and y = 25/7.